Matrix variate regressions and envelope models
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2018 · Volume 80 · Issue 2
Abstract
Modern technology often generates data with complex structures in which both response and explanatory variables are matrix valued. Existing methods in the literature can tackle matrix-valued predictors but are rather limited for matrix-valued responses. We study matrix variate regressions for such data, where the responseYon each experimental unit is a random matrix and the predictorXcan be either a scalar, a vector or a matrix, treated as non-stochastic in terms of the conditional distributionY|X. We propose models for matrix variate regressions and then develop envelope extensions of these models. Under the envelope framework, redundant variation can be eliminated in estimation and the number of parameters can be notably reduced when the matrix variate dimension is large, possibly resulting in significant gains in efficiency. The methods proposed are applicable to high dimensional settings.
Keywords
Matrix-valued response, Matrix variate regression, Reducing subspace, Sufficient dimension reduction
Enable JavaScript for citation tools and additional paper interactions.